Some Sufficient Conditions for Starlikeness and Convexity of Order

Yi-Ling Cang,Jin-Lin Liu

doi:10.1155/2013/869469

Abstract

We derive certain sufficient conditions for starlikeness and convexity of order of analytic functions in the unit disk. Applications are indicated for the subordination results to electromagnetic cloaking.

Highlights

Let A(p) denote a class of functions f(z) of the form ∞f (z) = zp + ∑ ap+nzp+n (p ∈ N = {1, 2, 3, . . .}), (1)n=1 which are analytic in the open unit disk U = {z ∈ C : |z| < 1}
N=1 which are analytic in the open unit disk U = {z ∈ C : |z| < 1}
By taking p = λ = 1 in Theorem 4, we have the following result which is due to Lin and Owa [2]

Summary

Introduction

We derive certain sufficient conditions for starlikeness and convexity of order α of analytic functions in the unit disk. Applications are indicated for the subordination results to electromagnetic cloaking. Let A(p) denote a class of functions f(z) of the form A function f(z) in A(p) is said to be starlike of order α in U if it satisfies zf󸀠 (z) f (z)

Results

Conclusion